Discrete Gaussian Curvature Flow for Piecewise Constant Gaussian Curvature Surface
| Autor: | Yohei Yokosuka, Takashi Kagaya, Yoshiki Jikumaru, Kazuki Hayashi, Makoto Ohsaki |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Surface (mathematics)
Physics 0209 industrial biotechnology Discretization Gaussian Mathematical analysis Form-finding 020207 software engineering 02 engineering and technology Computer Graphics and Computer-Aided Design Stationary point Industrial and Manufacturing Engineering Gaussian curvature flow Computer Science Applications Energy minimization symbols.namesake 020901 industrial engineering & automation Linear Weingarten surface Flow (mathematics) 0202 electrical engineering electronic engineering information engineering symbols Piecewise Gaussian curvature Discrete differential geometry Energy functional |
| Zdroj: | Computer-Aided Design. 134:102992 |
| ISSN: | 0010-4485 |
| DOI: | 10.1016/j.cad.2021.102992 |
| Popis: | A method is presented for generating a discrete piecewise constant Gaussian curvature (CGC) surface. An energy functional is first formulated so that its stationary point is the linear Weingarten (LW) surface, which has a property such that the weighted sum of mean and Gaussian curvatures is constant. The CGC surface is obtained using the gradient derived from the first variation of a special type of the energy functional of the LW surface and updating the surface shape based on the Gaussian curvature flow. A filtering method is incorporated to prevent oscillation and divergence due to unstable property of the discretized Gaussian curvature flow. Two techniques are proposed to generate a discrete piecewise CGC surface with preassigned internal boundaries. The step length of Gaussian curvature flow is adjusted by introducing a line search algorithm to minimize the energy functional. The effectiveness of the proposed method is demonstrated through numerical examples of generating various shapes of CGC surfaces. |
| Databáze: | OpenAIRE |
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